In underdoped cuprate superconductors, phase stiffness is low and long-range superconducting order is destroyed readily by thermally generated vortices (and anti-vortices), giving rise to a broad temperature regime above the zero-resistive state in which the superconducting phase is incoherent 1-4 . It has often been suggested that these vortex-like excitations are related to the normal-state pseudogap or some interaction between the pseudogap state and the superconducting state 5-10 . However, to elucidate the precise relationship between the pseudogap and superconductivity, it is important to establish whether this broad phase-fluctuation regime vanishes, along with the pseudogap 11 , in the slightly overdoped region of the phase diagram where the superfluid pair density and correlation energy are both maximal 12 . Here we show, by tracking the restoration of the normal-state magnetoresistance in overdoped La 2−x Sr x CuO 4 , that the phase-fluctuation regime remains broad across the entire superconducting composition range. The universal low phase stiffness is shown to be correlated with a low superfluid density 1 , a characteristic of both underdoped and overdoped cuprates 12-14 . The formation of the pseudogap, by inference, is therefore both independent of and distinct from superconductivity.In underdoped cuprates, an energy gap (pseudogap), of as yet unknown origin, appears in the electronic density of states well before superconductivity develops. The continuous evolution 6 of the pseudogap into the superconducting gap, combined with similarities in their gap magnitudes and symmetries 5 , has led to suggestions that the pseudogap is a precursor superconducting state 7-10 characterized by a broad temperature region over which the superconducting order parameter is finite but the phase fluctuates 3,4 . This picture of precursor pairing remains controversial however and is challenged by measurements indicating that the pseudogap itself closes at a critical doping concentration 11 , slightly beyond optimal doping, where superconductivity is most robust 12 . As it stands, there have been very few studies to date of the fluctuating superconductivity in overdoped, superconducting cuprates to establish the precise relationship between the pseudogap and phase fluctuation regimes.To address this, we focus here on the evolution of the upper critical field H c2 with temperature, as inferred by measurements of the in-plane resistivity ρ ab (T ,H ) in pulsed and d.c. magnetic fields. Previous transport studies in cuprates identified H c2 (T ) with the 'knee' at or near the top of the ρ ab (T ) curve or the temperature at which ρ ab (H ) attained a certain fraction of the normal-state value 15 . Either technique would lead to a H c2 (T ) line with a markedly different shape from that determined by the Nernst effect, for example. In this study, we adopt an alternative approach 16,17 , using the evolution of the transverse magnetoresistance ρ ab (H )(= ρ ab (H )− ρ ab (0) with H c) with temperature, field and doping, as ...